Context tree selection for functional data

TL;DR

This paper introduces a novel statistical method for analyzing EEG data to investigate whether the brain recognizes the underlying structure of auditory stimulus sequences generated by variable-length memory chains.

Contribution

It presents a new stochastic process model and a consistent model selection procedure for functional data, applied to EEG data to support the brain's ability to identify stimulus structure.

Findings

EEG data supports the hypothesis that the brain detects stimulus sequence structure.

The proposed model selection method is statistically consistent.

Experimental results align with the conjecture about brain statistical regularity retrieval.

Abstract

It has been repeatedly conjectured that the brain retrieves statistical regularities from stimuli. Here we present a new statistical approach allowing to address this conjecture. This approach is based on a new class of stochastic processes driven by chains with memory of variable length. It leads to a new experimental protocol in which sequences of auditory stimuli generated by a stochastic chain are presented to volunteers while electroencephalographic (EEG) data is recorded from their scalp. A new statistical model selection procedure for functional data is introduced and proved to be consistent. Applied to samples of EEG data collected using our experimental protocol it produces results supporting the conjecture that the brain effectively identifies the structure of the chain generating the sequence of stimuli.